Summary

The engaging Martin-Gay workbook series presents a reader-friendly approach to the concepts of basic math and algebra, giving readers ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the workbooks are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay enhances users' perception of math by exposing them to real-life situations through graphs and applications; and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book includes key topics in algebra such as linear equations and inequalities with one and two variables, systems of equations, polynomial functions and equations, quadratic functions and equations, exponential functions and equations, logarithmic functions an equations, rational and radical expressions, and conic sections. For professionals who wish to brush up on their algebra skills.

Table of Contents

Preface

ix

Prealgebra Review

1

(1)

Chapter R Pretest

2

(1)

Factors and the Least Common Multiple

3

(6)

Fractions

9

(10)

Decimals and Percents

19

Chapter R Activity: Interpreting Survey Results

28

(1)

Chapter R Vocabulary Check

29

(1)

Chapter R Highlights

30

(3)

Chapter R Review

33

(2)

Chapter R Test

35

Real Numbers and Introduction to Algebra

1

(80)

Chapter 1 Pretest

2

(1)

Tips for Success in Mathematics

3

(6)

Symbols and Sets of Numbers

9

(12)

Exponents, Order of Operations, and Variable Expressions

21

(10)

Adding Real Numbers

31

(8)

Subtracting Real Numbers

39

(10)

Integrated Review--Operations on Real Numbers

47

(2)

Multiplying and Dividing Real Numbers

49

(12)

Properties of Real Numbers

61

(20)

Chapter 1 Activity: Analyzing Wealth

69

(2)

Chapter 1 Vocabulary Check

71

(1)

Chapter 1 Highlights

71

(4)

Chapter 1 Review

75

(4)

Chapter 1 Test

79

(2)

Equations, Inequalities, and Problem Solving

81

(100)

Chapter 2 Pretest

82

(1)

Simplifying Expressions

83

(8)

The Addition Property of Equality

91

(10)

The Multiplication Property of Equality

101

(8)

Further Solving Linear Equations

109

(12)

Integrated Review--Solving Linear Equations

119

(2)

An Introduction to Problem Solving

121

(12)

Formulas and Problem Solving

133

(10)

Percent, Ratio, and Proportion

143

(12)

Linear Inequalities and Problem Solving

155

(26)

Chapter 2 Activity: Investigating Averages

168

(1)

Chapter 2 Vocabulary Check

169

(1)

Chapter 2 Highlights

169

(4)

Chapter 2 Review

173

(4)

Chapter 2 Test

177

(2)

Cumulative Review

179

(2)

Graphing Equations and Inequalities

181

(86)

Chapter 3 Pretest

182

(1)

Reading Graphs and the Rectangular Coordinate System

183

(20)

Graphing Linear Equations

203

(12)

Intercepts

215

(10)

Slope

225

(18)

Integrated Review--Summary on Linear Equations

241

(2)

Graphing Linear Inequalities in Two Variables

243

(24)

Chapter 3 Activity: Finding a Linear Model

252

(1)

Chapter 3 Vocabulary Check

253

(1)

Chapter 3 Highlights

253

(4)

Chapter 3 Review

257

(6)

Chapter 3 Test

263

(2)

Cumulative Review

265

(2)

Exponents and Polynomials

267

(76)

Chapter 4 Pretest

268

(1)

Exponents

269

(12)

Negative Exponents and Scientific Notation

281

(10)

Introduction to Polynomials

291

(10)

Adding and Subtracting Polynomials

301

(6)

Multiplying Polynomials

307

(6)

Special Products

313

(8)

Integrated Review--Exponents and Operations on Polynomials

319

(2)

Dividing Polynomials

321

(22)

Chapter 4 Activity: Modeling with Polynomials

329

(2)

Chapter 4 Vocabulary Check

331

(1)

Chapter 4 Highlights

331

(4)

Chapter 4 Review

335

(4)

Chapter 4 Test

339

(2)

Cumulative Review

341

(2)

Factoring Polynomials

343

(70)

Chapter 5 Pretest

344

(1)

The Greatest Common Factor

345

(8)

Factoring Trinomials of the Form x2 + bx + c

353

(6)

Factoring Trinomials of the Form ax2 + bx + c

359

(6)

Factoring Trinomials of the Form ax2 + bx + c by Grouping

365

(4)

Factoring by Special Products

369

(12)

Integrated Review--Choosing a Factoring Strategy

379

(2)

Solving Quadratic Equations by Factoring

381

(10)

Quadratic Equations and Problem Solving

391

(22)

Chapter 5 Activity: Factoring

400

(1)

Chapter 5 Vocabulary Check

401

(1)

Chapter 5 Highlights

401

(4)

Chapter 5 Review

405

(4)

Chapter 5 Test

409

(2)

Cumulative Review

411

(2)

Rational Expressions

413

(76)

Chapter 6 Pretest

414

(1)

Simplifying Rational Expressions

415

(8)

Multiplying and Dividing Rational Expressions

423

(10)

Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator

433

(8)

Adding and Subtracting Rational Expressions with Different Denominators

Excerpts

About This Book Algebra A Combined Approach,Second Edition is intended for a two semester course in introductory and intermediate algebra. It was written to provide asolid foundationin algebra for students who might have had no previous experience in algebra. Specific care was taken to ensure that students have the mostup-to-date relevanttext preparation for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. As suggested by the AMATYC Crossroads Document and the NCTM Standards (plus Addenda), real-life and real-data applications, data interpretation, conceptual understanding, problem solving, writing, cooperative learning, appropriate use of technology, mental .mathematics, number sense, critical thinking, and geometric concepts are emphasized and integrated throughout the book. The many factors that contributed to the success of the first edition have been retained. In preparing the Second Edition, I considered comments and suggestions of colleagues, students, and many users of the prior edition throughout the country. Algebra A Combined Approach,Second Edition is part of a series of texts that can includeBasic College Mathematics,Second Edition;Prealgebra,Third Edition;Introductory Algebra,Second Edition; andIntermediate Algebra,Second Edition. Throughout the series pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses. Key Pedagogical Features and Changes in the Second Edition Readability and Connections.I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problem-solving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information. In addition, each section begins with a list of objectives covered in the section. Clear organization of section material based on objectives further enhances readability. Problem-Solving Process.This is formally introduced in Chapter 2 with a four-step process that is integrated throughout the text. The four steps areUnderstand, Translate, Solve,andInterpret.The repeated use of these steps in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' comfort level and confidence in tackling problems. Applications and Connections.Every effort was made to include as many interesting and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. In the Second Edition, the applications have been thoroughly revised and updated, and the number of applications has increased. The applications help to motivate students and strengthen their understanding of mathematics in the real world. They show connections to a wide range of fields including agriculture, allied health, anthropology, art, astronomy, biology, business, chemistry, construction, consumer affairs, earth science, education, entertainment, environmental issues, finance, geography, government, history, medicine, music, nutrition, physics, sports, travel, and weather. Many of the applications are based on recent real data. Sources for data include newspapers, magazines, publicly held companies, government agencies, special-interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included. See the Applications Index on page xx. Practice Problem